Comparison of stochastic lung deposition fractions with experimental data

$: Comparison of stochastic lung deposition fractions with experimental data$
Ann. Occup. Hyg., pp. 1–14� The Author 2011. Published by Oxford University Press

on behalf of the British Occupational Hygiene Societydoi:10.1093/annhyg/mer100

Comparison of Stochastic Lung Deposition Fractionswith Experimental DataHUSSAIN MAJID1,2*, WERNER HOFMANN2 andRENATE WINKLER-HEIL2

1Division of Physics and Biophysics, Department of Materials Research and Physics, University ofSalzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria; 2Higher Education Commission, 44000Islamabad, Pakistan

Received 18 June 2011; in final form 21 September 2011

Deposition fractions of inhaled particles predicted by different computational models varywith respect to physical and biological factors and mathematical modeling techniques. Thesemodels must be validated by comparison with available experimental data. Experimental datasupplied by different deposition studies with surrogate airway models or lung casts were usedin this study to evaluate the stochastic deposition model Inhalation, Deposition and Exhalationof Aerosols in the Lung at the airway generation level. Furthermore, different analyticalequations derived for the three major deposition mechanisms, diffusion, impaction, andsedimentation, were applied to different cast or airway models to quantify their effect on cal-culated particle deposition fractions. The experimental results for ultrafine particles (0.00175and 0.01) were found to be in close agreement with the stochastic model predictions; however,for coarse particles (3 and 8 mm), experimental deposition fractions became higher with in-creasing flow rate. An overall fair agreement among the calculated deposition fractions forthe different cast geometries was found. However, alternative deposition equations resultedin up to 300% variation in predicted deposition fractions, although all equations predictedthe same trends as functions of particle diameter and breathing conditions. From this compar-ative study, it can be concluded that structural differences in lung morphologies among differ-ent individuals are responsible for the apparent variability in particle deposition in eachgeneration. The use of different deposition equations yields varying deposition results causedprimarily by (i) different lung morphometries employed in their derivation and the choiceof the central bifurcation zone geometry, (ii) the assumption of specific flow profiles, and(iii) different methods used in the derivation of these equations.

Keywords: bronchial airway models; experimental studies; lung casts; particle deposition equations

INTRODUCTION

Various modeling techniques have been applied topredict particle deposition fractions throughoutbronchial and alveolar airway generations. However,deposition fractions predicted by different models varywith respect to physical (fluid dynamics of the inhaledair) and biological (lung morphology and respiratoryphysiology) factors as well as mathematical modelingtechniques. Therefore, it is necessary to validate simu-

lated deposition fractions with experimental data forspecified aerosol parameters at defined flow rates.

Experimental deposition data supplied by deposi-tion studies in surrogate airway models or lung castsof upper bronchial airway generations (Schlesingeret al., 1982; Gurman et al., 1984; Cohen et al.,1990; Smith et al., 2001) are available for compari-son studies at the airway generation level. Availableairway cast geometries can further be used to quan-tify the observed variation in deposition fractions asdescribed by different studies. Advantages of con-ducting in vitro aerosol deposition studies with rep-lica casts and airway models include the accurate

*Author to whom correspondence should be addressed.Tel: +43-662-8044-5718; Fax: þ43-662-8044-150; e-mail:[email protected]

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control of airflow rates, the ability to precisely mea-sure deposition efficiencies, and the assessment oflocal deposition distributions and ‘hot spots’. There-fore, it is important to know the differences in depo-sition patterns between models and experiments inrealistic airway casts to understand the apparentdiscrepancies in deposition fractions.

In a previous study, Hofmann et al. (1998, 2002)investigated the effect of inter-subject variability ofairway dimensions in the thoracic region on totaldeposition fraction. Here, we compared the experi-mental deposition measurements in different humanlung airway casts with the stochastic modeling pre-dictions using the Monte Carlo deposition code Inha-lation, Deposition and Exhalation of Aerosols in theLung (IDEAL) (Hofmann and Koblinger, 1990;Koblinger and Hofmann, 1990) at the generationlevel (up to seven generations). Lung geometriesobtained from lung casts were implemented intothe IDEAL code to study their effect on particle de-position. We also investigated the effect of differentdeposition equations for diffusion, sedimentation,and impaction on particle deposition.

MATERIALS AND METHODS

In this study, deposition fractions were calculatedfor the first seven tracheobronchial (TB) airway gen-erations (trachea 5 Generation 1) measured duringdifferent experimental studies. Deposition fractionis defined as the ratio of the number of particles de-positing in a given generation to the number enteringthe first generation. Deposition in the nose andmouth is not considered here. Deposition fractionswere compared with experimental measurements ofSmith et al. (2001) for ultrafine particles and withGurman et al. (1984) for coarse particles. Similarly,lung cast geometries supplied by different surrogateairway models or lung casts were employed to quan-tify their effects on deposition. Since experimentaldeposition data are available for a variety of aero-sol diameter and breathing parameters, depositionwas calculated using the IDEAL code for thesegeometries under specified aerosol and flow rates.Deposition fractions for the implemented castgeometries were calculated for the inhaled unitdensity spherical monodisperse particles with di-ameters of 0.0017, 0.04, 0.01, 0.2, 3, and 8 lm tocover diffusion, sedimentation, and impaction re-gimes. Deposition was calculated for uniform in-spiratory flow rates of 15, 18, 20, 30, 34, and 40l min�1, splitting symmetrically between the twodaughter airways.

To investigate the effect of different depositionequations on deposition, several analytical equationsderived for the major deposition mechanisms(diffusion, sedimentation, and impaction) were im-plemented into the IDEAL code. These depositionequations, listed in the following sections, were usedto determine the deposition fractions for each castgeometry along with the stochastic lung geometry.

The stochastic lung model IDEAL is derivedfrom measured morphometric data reflecting theasymmetric nature of the branching pattern of thelung and the statistical relationships between parentand daughter airway parameters (Koblinger andHofmann, 1985). The IDEAL code was temporarilymodified for different cast geometries and deposi-tion equations for comparison purposes. The mainadvantage of the stochastic deposition modelIDEAL is the calculation of deposition at eachsingle airway generation level by the applicationof the most realistic lung structure presently avail-able in terms of dimensional variability and branch-ing asymmetry. The simulations of each inspiredparticles through a stochastic asymmetric lungstructure by randomly selecting a sequence ofairways using Monte Carlo Methods allows thecalculation and quantification of the distributionsof deposition fractions due to intra- and inter-subject variability rather than only average values.This specific feature of the stochastic lung modelleads to significant variability in depositionfractions within a given airway generation and alsoa varying number of airway generations alonga randomly selected path.

This type of model differs qualitatively fromothers developed over the past half-century. Forexample, a deposition model produced by the Inter-national Commission on Radiological Protection(ICRP, 1994) calculates the average depositionfractions at regional level (two extrathoracic, i.e.nasal and oral passages, bronchial, bronchiolar, andalveolar regions) and it is easy to use with less com-putational work. Multiple-path models (Anjilvel andAsgharian, 1995) are more realistic than semi-empirical (ICRP, 1994) and deterministic models[single-path model, e.g. Weibel (1963), Yeh andSchum (1980), and trumpet model, e.g. Taulbeeand Yu (1975)] because they are based on actualairway measurements rather than on averagevalues, and thus capture the asymmetric branchingpattern and hence flow rates in the lung. However,a complete deterministic asymmetric description ofthe human lung is presently not available in multi-ple-path models and is restricted to the upperairways (Cassee et al., 1999).

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Experimental data of different lung casts

Several geometrical lung models of the human re-spiratory system have been employed to calculatethe deposition of ambient aerosols (Weibel, 1963;Soong et al., 1979; Yeh and Schum, 1980; Koblingerand Hofmann, 1990), leading to a range of deposi-tion fractions. Thus, different casts were producedto obtain more reliable experimental informationon deposition and dose distribution in the humanlung. Unfortunately, such experimental data are lim-ited to the upper bronchial airways due to technicallimitations in cast production. The various castmeasurement studies, which were implemented inIDEAL to study their effect on deposition, arediscussed below. The characteristic dimensionsobtained from these studies are given in Table 1.

A hollow silicon rubber cast prepared from au-topsy specimens (normal lung of a 54-year-oldwoman) of the human TB tree for the study of parti-cle deposition was developed by Schlesinger andLippmann (1972) and Schlesinger et al. (1982). De-position studies were carried out for coarse particles(2.5–8 lm). The airways were assigned generationnumbers according to the lung model of Weibel(1963). The laryngeal jet was considered in these ex-periments to simulate the effect of the larynx on de-position in the first few generations. Gurman et al.(1984) conducted their experiment on depositionusing the same lung cast.

Cohen et al. (1990) carried out deposition experi-ments in replicate hollow casts of the upper airwaysof a 34-year-old man’s TB tree using ultrafine par-ticles (,0.2 lm) for a variable larynx. The castingprocess and replicate production in that studywere carried out using the methods described bySchlesinger et al. (1982). The length and diameterof the airways were smaller than those of Yeh andSchum (1980). The airways were again assignedgeneration numbers according to Weibel’s (1963)model.

A silicon rubber cast of the respiratory tract wasmade by Yamada et al. (1994) for a normal humanadult. The model consisted of the trachea and themain bronchi with branching generations from 4 to10 and each individual airway segment was assigneda unique binary identification number using the sys-tem designed by Raabe et al. (1976). This study wasconducted for ultrafine particles with diameters,0.1 lm where diffusion is the dominant depositionmechanism.

Replicate casts of the larynx and five to eightgenerations of a 23-year-old male human’s TB tree,obtained by autopsy, were produced by Smith et al. Tab

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Comparison stochastic particle lung deposition 3 of 14

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(2001). The production mould for this cast was madeof silicone rubber. A light coat of oil was applied tothe interior of the models to simulate the mucous lin-ing of the TB tree. The individual airways were iden-tified using the numbering scheme proposed by Raabeet al. (1976). That study was conducted to determinethe deposition patterns of nanometre-sized particles inthe TB airways. The results obtained by Smith et al.(2001) verified the experimental findings of Cohenet al. (1990), which showed a higher diffusional depo-sition in cylindrical tubes than theoretical predictions.

The anatomical data (airway dimensions andbranching angles) of the above-mentioned castswere employed to calculate deposition fractions forboth ultrafine and fine particles. The airways wereassigned generation numbers according to themostly used Weibel’s (1963) model.

Application of different deposition equations

Three basic deposition mechanisms (Brownianmotion, impaction, and sedimentation) play a majorrole in the TB region. For particles with diametersdp � 0.5 lm, deposition in the TB region is predom-inantly caused by the diffusion mechanism, while forparticle sizes dp . 0.5 lm, deposition is causedprimarily by both impaction and sedimentation.Various deposition equations have been derived bya number of scientists to estimate deposition frac-tions in the TB region.

Deposition by diffusion

Equation formulated by Yeh and Schum. For lami-nar parabolic flow conditions, Yeh and Schum(1980) derived the following deposition equation:

gD 5 1 � 0:819e� 7:315x � 0:0976e� 44:61x

� 0:0325e� 114x � 0:0509e� 79:3x2=3

; ð1Þ

where x5LD�

2R2�v;, R (cm) is the radius of airwaytube, �v (cm s–1) is mean flow velocity, and L (cm)is length of airway tube, and D is the particle diffu-sion coefficient.Equation formulated by Cohen and Asgharian. For

a replica cast of the upper bronchial airways, Cohenand Asgharian (1990) derived the following empiri-cal equation for enhanced diffusion deposition ofultrafine particles in the turbulent region due to thebranching of airways as follows:

gD 5 2:965D0:568; ð2Þwhere D 5 p lD/4Q; l is the airway length, D is thediffusion coefficient, and Q is the flow rate measuredin ml s�1.

Equation formulated by Ingham. Ingham (1991)derived the following equation theoretically for thedeposition efficiency in the human airways forlaminar developing flow conditions:

gD 5 4:458D0:55Sc� 0:111; ð3Þwhere Sc5t=D is the Schmidt number, with particlediffusion coefficient D, and fluid kinematic viscosity,m.Equation formulated by Yu and Cohen. Yu and

Cohen (1994) derived the following efficiencyequation for deposition on the basis of their experi-ments by considering the laminar developing flowconditions:

gDth 5 aRebScc�l

R

�d

5 a

�2V

Rpv

�� mD

�c�l

R

�d

; ð4Þ

where Re is Reynolds number. The best fitted valuesof constants a, b, c, and d to the experimental datafound by Yu and Cohen (1994) are:

a5 1:2027; b5 � 0:6067;

c5 � 0:5108; d5 0:50081

In the trachea, the deposition data measured weresubstantially higher than the bronchial data due to theeffect of the laryngeal jet. Thus, for tracheal deposition,the following enhanced values of constants were used:

a5 20630; b5 � 2:2004; c5 � 0:2339; d5 1:0

Equation formulated by Martonen et al. Martonenet al. (1996) solved the momentum and concentra-tion equations analytically using a scaling techniqueto develop a theoretical model for particle diffusionfor developing flows within airways. The effect ofthe curvature of the tube has been considered when de-riving the equation, which has improved accuracy ofthe model. The equation is of the form:

gD 5 3:89D1=2Sc� 1=6; ð5Þwhere D is the dimensionless diffusion parameter de-fined as D 5 DL/4UR2, where U is the average inletvelocity and L is the developing velocity profilelength.Equation formulated by Broday. Broday (2004) de-

veloped an expression for the average diffusive fluxtoward the airway wall based on similarity solutionsfor both the velocity and the concentration fields inthe respective boundary layers that develop adjacentto the surface of a plane wedge. The expression forthe deposition efficiency compares favorably to thoseobtained by rigorous computational fluid dynamicssimulations and account for different branching an-gles, airflow rates, and particle sizes.


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gD 5 1:6Re� 1=2

�2R0

l

�� 1

Sc� 2=3; ð6Þ

where R0/l is the ratio of the radius of the parent tubeto the length of the daughter tube.

Deposition by impaction

Equation formulated by Johnston and Schroter.Johnston and Schroter (1979) derived the followingformula for impaction deposition probability calcula-tions:

PðIÞ5 8:5 � 103qRe9

�dp2R

�2:5

sin3h; ð7Þ

where Re9 is the parent airway Reynolds number, dp

is the particle diameter, q is the particle density, R isthe airway radius, and h is the airways branchingangle in radians.Equation formulated by Yeh and Schum. Yeh and

Schum (1980) derived the following impaction de-position equation for laminar parabolic flow profile:

P�I�5 1 � 2

pcos� 1ðhStÞ þ 1psin½2cos� 1ðhStÞ� for h St,1;

P1 5 1 for h St � 1

ð8Þwhere St5Ccqdp�v

�18lR is the stokes number with

the particle slip correction factor Cc and air absoluteviscosity l.Equation formulated by Martonen et al. The

equation for the impaction deposition probability de-rived by Martonen et al. (1985) for laminar parabolicflow is given as under:

PðIÞ5 2

p

he�1 � e2

�1=2 þ arcsinðeÞi; ð9Þ

while for turbulent flow conditions, it is:

PðIÞ5 1 � exp

�� 4e

p

; ð10Þ

with e 5 hs U/2R, where h is the branching angle, Uis the mean air velocity, R the airway radius, ands 5 mCc/3plD the particle relaxation time, whereD is the particle diffusion coefficient.Equation formulated by GawronskI and Szewc-

zyk. Gawronski and Szewczyk (1986) using conceptof stopping distance derived the following equationfor bent tubes for inertial impaction deposition:

PðIÞ5 16

3p/:St

2 �

�4

3/:St

�1=2�; ð11Þ

where U 5 2(R/R0) sinh, h is the branching angle, Ris the radius of the daughter branch, and R0 is the ra-dius of the parent branch.

Equation formulated by Zhang et al. Zhang et al.(1997) derived the following deposition equation forcylindrical tubes by impaction:

PðIÞ5 0:000654expð55:7Stk0:954ÞRe1=3sinh for Stk,0:45

�0:19 � 0:193exp

�� 9:5Stk1:565

� Re1=3sinh for Stk � 0:04

ð12Þfor parabolic flow and

PðIÞ5 0:000425exp�22:7Stk0:832

�Re1=3sinh for Stk,0:07

5�0:19 � 0:194exp

�� 3:28Stk1:585

� Re1=3sinh for Stk � 0:07

ð13Þfor uniform inflow.

Deposition by sedimentation

Equation formulated by Pich.

For fully developed laminar parabolic flow in hor-izontal tubes, Pich (1972) proposed the followingsedimentation deposition equation:

PðSÞ5 2

p

h2e

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 � e2=3

p� e1=3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 � e2=3

pþ arcsinðe1=3Þ

i; ð14Þ

where e53vsl=8RU, vs the particle settling velocity, lthe tube length, U the average flow velocity, and R thetube radius. For inclined tubes, with vs

usin/,,1, thedeposition efficiency can be calculated using aboveformula with e53vsL

8rUcos/, where / is the gravityangle.Equation formulated by Yu et al. Yu et al. (1977)

derived an equation to calculate deposition in a hori-zontal circular channel for laminar parabolic uniformflow by solving the governing equation for simulta-neous sedimentation and diffusion. For negligible dif-fusion, the deposition efficiency equation reduces to:

PðSÞ5 2

p

24Sin� 1

�4

3

�e � 4

3e

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 �

�4

3e

�2s 3

5; ð15Þ

Equation formulated by Yeh and Schum. Deposi-tion by sedimentation, formulated by Yeh andSchum (1980), is given as under:

PðSÞ5 1 � exp

"� 4gCqpr

2pLcos/

9plR�v

#; ð16Þ

where g is the acceleration of gravity, U is theangle relative to gravity, qp is the density of the parti-cle, C is the Cunningham slip correction factor, rp isthe particle radius, and l is the viscosity of the fluid.Equation formulated by Martonen et al. Martonen

et al. (1985) formulated the following equation forsedimentation deposition probability consideringlaminar parabolic flow conditions:


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PðSÞ5 2

p

he�1 � e2

�1=2 þ arcsinðeÞi; ð17Þ

with e5tVcos/=2R, where t is the residence time inthe respective airway generation, vs is the particleterminal settling velocity, and U is the airway anglerelative to gravity.

For turbulent flow conditions, the sedimentationdeposition probability with gravitational constantg is:

PðSÞ5 1 � exp

�� 2sgtcos/

pR

; ð18Þ

where g is the gravitational constant.

RESULTS AND DISCUSSION

Comparison with experimental measurements

The deposition dominated by diffusion was deter-mined experimentally for 0.00175-, 0.01-, and0.04-lm particles at flow rates of 20 and 40 l min�1

by Smith et al. (2001). Deposition results obtainedfor adult replica cast were compared with stochasticlung deposition models with the same aerosol andbreathing conditions. Experimental measurementsfor 0.00175- and 0.01-lm particles were found tobe in close agreement with the stochastic modelpredictions with a ratio of 1.08 and 1.02, respectively;however, experimental deposition fractions for 0.04-lm particles were up to seven times higher than thepredictions at the low flow rate (Fig. 1). At high flowrates, impaction deposition probably contributes tothe increased deposition of 0.04-lm particles duringexperiments as compared to smaller particles.

The experimental deposition in upper airway gen-erations is somewhat higher than that predicted bythe stochastic model due to complicated plug flowconditions. The variation between the experimentaland calculated deposition fractions at the generationlevel are attributed to the variations in geometricalstructures employed and the flow profile assump-tions. A sharp dip at Generation 4 for ultrafine par-ticles is seen in experimental data of Smith et al.(2001); however, no such dip is observed in predic-tions by the stochastic lung model. Smith et al.(2001) illustrate these inhomogeneities to the re-peated bifurcation airway system where flow profileis complicated and cannot be described either by par-abolic or by plug flows.

The measured results of Smith et al. (2001) agreewith the measurements of Cohen et al. (1990), whoshowed that the measured deposition is higher thanthat predicted assuming plug flow for diffusional de-position in circular tubes, owing to a fully developedparabolic flow profile assumption. However, theobservation by Cohen et al. (1990) of increased de-position in the trachea at low flow rates comparedto higher flow rates is not consistent with thestochastic lung predictions.

The deposition by impaction was determined byGurman et al. (1984) for 3- and 8-lm particles at flowrates of 15 and 30 l min�1, respectively. The sameaerosol and flow data were used to calculate deposi-tion fractions by the stochastic lung model. At a flowrate of 15 l min�1, experimental measurements for3-lm particles were close to the predicted results,but for the 8-lm particles, the experimental resultswere two times higher than the predicted values.These variations were more enhanced at a higher flow

Fig. 1. Comparison of experimental and calculated deposition fractions up to Generation 8 for different ultrafine particle sizes andflow rates.


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rate. Flow rate seems to be the major influencing fac-tor for the apparent variations in deposition fraction inaddition to airway dimensions employed in both stud-ies (Fig. 2). At high flow rates, large particles are un-able to follow the airstream lines. Since Gurman et al.(1984) used cyclic flow containing higher peak veloc-ities, it is likely that during peak velocities, the flow inthe casts becomes unstable at bifurcations sites,imparting additional inertial force to the larger par-ticles and hence resulting in enhanced deposition byimpaction. Enhanced deposition may also be attrib-uted to the formation of secondary flow at carinalridges (the shape of the edges dividing the parent tubeinto daughter tubes at bifurcations sites) at high flowrates. However, at low flow rates (20 l min�1), the var-iation in the deposition fraction is not that evident. Onthe other hand, analytical deposition equations used in

model predictions refer to straight cylindrical tubesand are not able to account for the effect of local scaleinhomogeneities on particle deposition within anairway or an airway bifurcation.

Calculated deposition fractions for different castgeometries

The comparison of mean deposition fractions ineach of the first six to seven generations includingthe trachea is shown in Fig. 3. Deposition calculationswere performed for 0.2-lm sized particles at a flowrate of 15 l min�1 and for 3-lm particles at a flow rateof 34 l min�1. Significant differences were observedfor both particle sizes and flow rates due to differentairway dimensions. While deposition is higher forsmaller cross-sectional areas of the generations, aver-age deposition fractions are compensated by their

Fig. 2. Comparison of experimental and calculated deposition fractions up to Generation 6 for different coarse particle sizes andflow rates.

Fig. 3. Deposition of particles in the first seven TB generations for two different particle sizes and flow rates, calculated fordifferent cast geometries.


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smaller surface areas in each generation, i.e. the largerthe surface area of a particular generation, the lowerthe average deposition fraction. Variations observedin the morphometric parameters (in length and diam-eters) of up to 45% led to corresponding variations inthe deposition of up to 250% for 0.2-lm particles and400% for 3-lm particles. Due to the consideration ofthe laryngeal jet during calculations, deposition in-creased in the first few generations. However, asthe flow started to become laminar, this enhanced de-position was reduced specially for large particles,where impaction deposition was dominant. Thetrachea is considered first generation here. Due tothe absence of a bifurcation in the first generation, de-position fractions are lower compared to the secondgeneration.

The stochastic model predicted a lower depositionfraction in Generations 2 and 3 for 0.2-lm particlesand a consistently lower deposition fraction for allseven generations for 3-lm particles when comparedto measurements with the surrogate airway models.Since airway diameters and lengths in each studyrefer to different people, they display an inherentbiological variability. The application of differentcasting and measurement techniques in these studiesmay have added an additional variability. Hence,structural differences of lung morphologies amongdifferent individuals seem to be largely responsiblefor the variability in particle deposition particularlyfor larger particles. Because of the large inter-subject

variability, the negative mean bias of the stochasticmodel relative to the surrogate models seen inFig. 3 is not considered significant.

The frequency distribution of the deposition frac-tions in airway Generation 4 calculated using theIDEAL code is plotted in Fig. 4 for 3-lm particlesat a flow rate of 34 l min�1. Since the effect ofvariability of airway geometry on the resulting vari-ability on deposition fractions is investigated, depo-sition fractions presented here are normalized to theparticles entering the trachea. In general, these distri-butions can reasonably be approximated by lognor-mal distributions. As a result of the variability inairway morphology and related flow rates, deposi-tion fractions are highly variable. Consequently,deposition fraction in each airway also exhibitsinter-subject variations (Fig. 4).

Effect of different deposition equations ongenerational deposition

Diffusion. Diffusion in the respiratory tract typi-cally occurs for particles ,0.1 lm in diameter, thediffusion coefficient being inversely proportional tothe particle’s physical diameter (Hinds, 1999).A number of diffusion equations (1–6) as listed inthe previous sections were employed to see their ef-fect on particle deposition in a variety of TB airwaycast geometries for particles of diameter 0.04 lmand at a flow rate of 18 l min�1. The derivationmethod and the specific flow conditions considered

Fig. 4. Probability distribution of the deposition fractions of 3-lm particles in airway Generation 4 at a flow rate of 34 l min�1.


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during derivation of diffusion equations largely af-fected the deposition fractions. For example, Ingham(1991) theoretically derived the deposition effi-ciency in a cylindrical tube for parabolic laminarflow conditions. In contrast, the equation by Cohenand Asgharian (1990) was derived from a fit toexperimental data, thereby taking into account non-laminar or developing flow conditions. Increaseddeposition occurs at turbulent flow as compared tolaminar flow conditions. These flow conditions be-come further complicated by the choice of central bi-furcation geometry where branching of airwaystakes place, resulting in the formation of secondaryflows (Hofmann et al., 2003).

The trend of deposition fractions produced by dif-ferent deposition equations is similar in the firstseven generations, except for the equation by Cohenand Asghrian (1990), which considers the turbulencein upper airway generations and hence high deposi-tion efficiency (Fig. 5). Up to 100% variation in de-position fractions by different diffusion depositionscould be observed.

The equations of Yeh and Schum (1980) producedthe highest deposition fraction in the thoracic region(Fig. 8), whereas the equation by Broday (2004), inwhich a wedge-shaped bifurcation is consideredwith average diffusive flux and laminar flow condi-tions, produced minimum generational deposition,i.e. almost 50% of deposition predicted by Yeh andSchum (1980). The equation of Ingham (1991),which considers fully developed laminar flow, pro-duced intermediate deposition fractions to that ofthe obtained minimum and maximum values.

Impaction

Inertial impaction occurs when airborne particlespossess enough momentum to keep its trajectorydespite changes in the direction of the airstream, con-sequently colliding with the walls of the airways. Thedimensionless Stokes number (Stk) controls the prob-ability of particle deposition in the airways by impac-tion. The higher the Stokes number, the higher theprobability of particle deposition by inertial impac-tion. Therefore, considering the bifurcation geometryof the lungs, large particles travelling through the air-ways at high airflow velocities are more likely to im-pact in the proximal portion of the respiratory tract(upper airways) (Zeng et al., 2001).

The impaction deposition for various lung geome-tries and deposition formulae was calculated for3-lm particles at a flow rate of 34 l min�1 (Fig. 6).The formula by Gawronski and Szewczyk (1986)yielded variable high deposition fractions in theupper airway generations in all cast geometries.

However, the equation by Johnston and Schroter(1979) predicted the highest total lung deposition frac-tion (Fig. 8). The cast geometry of Schlesinger et al.(1982) contained the smallest diameters for each gen-eration and thus produced the highest deposition byimpaction (Fig. 6d). Zhang et al. (1997) consideredthe Reynolds number with uniform flow in upperairway generations, thus producing relatively higherdeposition fractions. However, the distinct high peakfor the equation of Johnston and Schroter (1979) indistal generations is probably caused by the higherexponent for the daughter to parent diameter ratio(Fig. 8). Up to 300% variation in the deposition frac-tion by impaction deposition equations could beobserved. An overall close agreement was found be-tween the deposition fraction obtained by the equa-tions of Yeh and Schum (1980) and Martonen et al.(1985). The airway geometry of Schlesinger et al.(1982) showed relatively higher deposition fractionsin each generation due to deposition by impaction.

Sedimentation

Sedimentation is a time-dependent process thatoccurs when gravitational force acts on a particleand causes it to gradually move out of the airstreamline. If the weight of the particle is greater than thebuoyant force exerted by the fluid on it, it will quitits original streamline path. As the particle settles,it experiences a drag from the fluid, causing it toquickly reach a terminal settling velocity. Sedimen-tation is the dominant mechanism for larger particlesand low flow rates and is also dependent on thebranching angle and the airway geometry. The sedi-mentation deposition for various lung geometriesand deposition formulae was calculated for 3-lmparticles at a flow rate of 34 l min�1.

For the selected sedimentation equations, calcu-lated deposition fractions exhibited a similar trend,primarily due to the constant branching angle em-ployed in this study (see Fig. 7). Branching anglesfor cast studies were not available for most ofthe reports. Similarly, all sedimentation depositionequations employed in this study were derived forlaminar flow conditions, except for the equation ofYeh and Schum (1980), which was derived for uni-form flow. Deposition in all lung generations revealedthat sedimentation deposition is dominant in distalgenerations of the TB tree, where airway diametersare smaller and flow rates are slower (Fig. 8).

CONCLUSIONS

Measured lung airway cast geometries with upto seven generations obtained from four different


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experimental studies, deposition fractions and depo-sition equations for the major deposition mecha-nisms derived by various scientists were used hereto compare their results with that of the stochasticdeposition model IDEAL.

Deposition of ultrafine and coarse particles wascalculated at various flow rates to investigate theireffect on deposition. Experimental measurements(Smith et al., 2001) for ultrafine particles were foundto be in close agreement with the stochastic model

Fig. 5. Inspiratory deposition fractions for inhalation of 0.04-lm particles at a flow rate of 18 l min�1 Deposition was calculatedusing different diffusion equations and lung cast geometries of (a) Smith et al. (2001), (b) Yamada et al. (1994), (c) Cohen and

Asgharian (1990), (d) Schlesinger et al. (1982) in the first six generations, and (e) Koblinger and Hofmann (1990).


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predictions for 1.7-nm and 0.02-lm particles andwere up to seven times higher for 0.04-lm particles.The experimental results (Gurman et al., 1984) forcoarse particle sizes (3 and 8 lm) became higher

with increasing flow rate when compared to the sto-chastic predictions. An overall fair agreement amongthe deposition fractions for different cast geometrieswas found. However, variability in deposition

Fig. 6. Inspiratory deposition fractions for inhalation of 3-lm particles at a flow rate of 34 l min�1. Deposition was calculated bydifferent impaction equations and lung cast geometries of (a) Smith et al. (2001), (b) Yamada et al. (1994), (c) Cohen and



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fractions using different cast geometries arose due tostructural differences in lung morphologies, whichwere derived from different ethnic and aged subjects.The calculated Stokes and Reynolds numbers for

particular airway cast geometries are also responsi-ble for variable deposition fraction.

All implemented deposition equations predictedthe same deposition trends as functions of particle

Fig. 7. Inspiratory deposition fractions for inhalation of 3-lm particles at a flow rate of 34 l min�1. Deposition was calculated bydifferent sedimentation equations and lung cast geometries of (a) Smith et al. (2001), (b) Yamada et al. (1994), (c) Cohen and



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Fig. 8. Inspiratory deposition fraction for the three major deposition mechanisms using different deposition equations and thestochastic lung geometry (Koblinger and Hofmann, 1990). Deposition by diffusion was calculated for 0.2-lm particles at a flow rateof 15 l min�1, whereas deposition by impaction and sedimentation was calculated for 3-lm particles at a flow rate of 34 l min�1.


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diameter and breathing conditions. However, thevariations in the deposition fractions arose due tothe lung morphometry employed, the choice of thecentral bifurcation geometry (i.e. the branching an-gle and bifurcation shape), the consideration of spe-cific flow profiles (i.e. entrance effect), and themathematical methods employed in the derivationof the equations. Up to 100% variation in depositionfractions by diffusion deposition and up to 300%variation in deposition fraction by impaction deposi-tion could be observed. In contrast, different sedimen-tation equations produced similar deposition fractions.

FUNDING

This work was funded in part by EU contract no.516483 (Alpha Risk) and by Higher Education Com-mission of Pakistan under the scholarship program(Overseas Scholarships for Pakistani Nationals).

Acknowledgements—This work was supported by the HigherEducation Commission of Pakistan. The authors have noconflict of interest in the research presented in this manuscript.

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